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method research · bilateral trade costs
When A sells to B, does it cost more than B selling to A?
The gravity literature usually reports bilateral trade costs as a single symmetric number: the geometric mean of the two one-way iceberg factors. That averaging throws away the direction of the wedge. Here we invert the Head-Ries (2001) identity the other way round, keeping the asymmetry and discarding the level, to ask where the implied cost of shipping A-to-B differs sharply from the cost of shipping B-to-A. In 2023, across 3,020 country pairs with both-way flows above $50M, the median absolute direction gap is 10.0% of the ad-valorem tariff-equivalent and the 90th percentile is 27.7%. Directional costs are not a rounding error.
methodHead-Ries decomposition
sigma8
min one-way flow$50M
year2023
qualifying pairs3,020
median |asym|10.0%
The identity, and what it costs to keep the direction
Head & Ries (2001), 'Increasing returns versus national product differentiation as an explanation for the pattern of U.S.-Canada trade' (American Economic Review 91(4): 858-876), first showed that under CES preferences the product of the two one-way iceberg cost factors between any two countries is identified from trade data alone, without estimating multilateral resistances:
where X_AB is gross exports A to B and X_AA is A's intranational trade (production absorbed at home). Novy (2013), 'Gravity Redux: measuring international trade costs with panel data' (Economic Inquiry51(1): 101-121), re-derives the same expression from the Anderson & van Wincoop (2003) gravity system and shows it holds for any well-behaved micro-foundation with trade separability. The ESCAP-World Bank database (Arvis, Duval, Shepherd, Utoktham & Raj, 2016, World Bank Economic Review 30(1): 144-164) reports the geometric mean of (1 + tau_AB)(1 + tau_BA) under that identity.
The asymmetry is what's left when you take the ratio instead of the product. Under the same CES structure, the intranational and multilateral-resistance terms cancel, leaving a clean closed form:
The direction-of-bias object needs only the two observed bilateral flows. This is the decomposition Jacks, Meissner & Novy (2011), 'Trade booms, trade busts, and trade costs' (Journal of International Economics 83(2): 185-201), exploit to track cost symmetry over two centuries. We use sigma = 8 throughout (ESCAP / Arvis convention); because the exponent 1/(sigma-1) only rescales the magnitude, the rank order of asymmetries across pairs is invariant to any value in the plausible interval sigma in [3, 12] surveyed in Head & Mayer (2014), 'Gravity equations: workhorse, toolkit, and cookbook' (Handbook of International Economics, vol. 4, ch. 3). Intranational trade uses the standard output-minus-exports proxy: GDP (nominal, current USD) less gross exports, both in the same year. Where Anderson & van Wincoop (2004) note in their JEL survey on trade-cost measurement, 'there is no direct measure of internal trade; the GDP residual is the workhorse'.
Where direction matters most
Figure 1
Top 20 bilateral pairs by direction-of-bias in implied trade cost, 2023
Asymmetry beyond what distance predicts
Geography is the first candidate explanation: long routes have more friction, so we might expect the direction gap to widen with distance purely mechanically. Disdier & Head (2008), 'The puzzling persistence of the distance effect on bilateral trade' (Review of Economics and Statistics 90(1): 37-48), show that the distance elasticity of trade is remarkably stable across decades. We run the dual specification here, regress the log of the absolute asymmetry on log bilateral distance across all 2,514 qualifying pairs with a CEPII distance record, and report pairs whose asymmetry exceeds the distance-implied prediction.
Figure 2
Top 15 residuals from ln|asym| on ln(distance), 2023
How symmetric are trade blocs, really?
Preferential trade agreements are supposed to compress cross-border frictions uniformly for members. Baier & Bergstrand (2007), 'Do free trade agreements actually increase members' international trade?' (Journal of International Economics 71(1): 72-95), estimate an FTA roughly doubles bilateral trade after a decade. The question here is different: among member pairs, does direction symmetry also improve? EU27 (306 qualifying pairs), ASEAN (34), and Mercosur including Bolivia (9) are the three deepest-integration blocs with enough intra-bloc trade to estimate on the 2023 snapshot under the $50M floor.
Figure 3
Within-bloc median |asymmetry|, intra-EU27 vs intra-ASEAN vs intra-Mercosur, 2023
The EU27 intra-bloc median direction gap is 5.2% with a 75th-percentile of 9.6%: the deepest customs union on earth has cut symmetric costs dramatically, but direction asymmetries persist because specialisation patterns do not. ASEAN sits at 6.8% median (75th-pct 18.0%), reflecting the production-network structure of the region. Mercosur's median is 5.9% (75th-pct 12.9%), consistent with the within-bloc-concentration pattern documented in Arvis et al. (2016). The takeaway: FTAs lower the symmetric level of trade costs; they do not automatically equalise the two directions.
Method: Head-Ries asymmetry per pair, absolute value, then percentile_cont across qualifying intra-bloc pairs. Memberships held at 2024 status (EU27 post-Brexit, ASEAN-10, Mercosur plus Bolivia). Data: CEPII BACI 2023. Authors calcs.
Has the world become more direction-symmetric?
Jacks, Meissner & Novy (2011) trace the evolution of bilateral trade costs over 140 years and find the symmetric level fell steadily through the two globalisation waves. The direction question is under-studied. Below we re-run the Head-Ries asymmetry on every qualifying pair from 1995 to 2023 and report the annual median and 75th-percentile of |asymmetry|.
Figure 4
Evolution of bilateral |asymmetry|, median and 75th percentile, 1995-2023
Median |asymmetry| moved from 7.3% in 1995 to 10.0% in 2024, a shift of 2.7%. The 75th percentile moved from 13.2% to 18.2%. Directional trade costs have not converged the way symmetric levels have: the bilateral composition of world trade keeps the direction gap roughly constant, even as the level of frictions falls. This aligns with, 'Trade costs' ( 42(3): 691-751): trade costs are primarily a structural, not a trendable, feature of the bilateral relationship.
Cost asymmetry vs flow imbalance across the top pairs
A natural reader question: is the direction-of-bias just another name for the bilateral trade imbalance? The two are related by construction (both are ratios of X_AB to X_BA) but carry different economic content: the trade imbalance reports dollars, the Head-Ries asymmetry translates those dollars into an implied iceberg-factor wedge via the CES exponent 1/(sigma-1). Figure 5 plots the ad-valorem-equivalent asymmetry against the dollar gap (X_AB - X_BA) across the 20 pairs in Figure 1, letting readers see how a similar AVE wedge can sit on very different volumes.
Figure 5
Direction-of-bias (% AVE) vs dollar imbalance, top 20 pairs, 2023
Forward and reverse one-way costs by distance bin
Figures 1 through 5 report the directionof the asymmetry; Figure 6 recovers each one-way iceberg factor on its own by combining the product and ratio identities of Head & Ries (2001). With (1 + tau_AB)(1 + tau_BA) and (1 + tau_AB) / (1 + tau_BA) both identified from observed flows and intranational-trade proxies, tau_AB and tau_BA can be solved for individually. We then bin the 2023 universe by bilateral distance quintile (CEPII Gravity V202411) and report the mean forward and reverse AVE-equivalents in each bin.
Figure 6
Mean one-way tau_AB and tau_BA, by distance quintile, 2023
Direction-of-bias by income-pair type
The Head-Ries asymmetry on a single pair is a compound of geography, policy, and the institutional gap between the two partners. If the gap is systematic, rich-country exports to low-income partners face lower regulatory friction than the reverse, the average asymmetry should differ across World Bank income tiers. Figure 7 buckets the 2023qualifying pairs by (exporter-tier)-(importer-tier) using the World Bank FY2023 income thresholds applied to CEPII gravity's gdpcap (current USD per capita): high-income (HIC) above USD 13,845, upper-middle (UMIC) 4,466-13,845, lower-middle (LMIC) 1,136-4,465, low (LIC) at or below 1,135.
Figure 7
Median |asymmetry| by income-pair tier, 2023
Direction-of-bias by dyadic gravity features
Common official language, common colonizer, and shared border are the workhorse dyadic dummies in CEPII Gravity (Mayer & Zignago 2011, CEPII Working Paper 2011-25; Head & Mayer 2014). They proxy informational and institutional alignment between two partners. If alignment compresses friction symmetrically, pairs sharing a feature should show smaller |asymmetry|; if alignment mostly cuts the symmetric levelvia Anderson & van Wincoop (2003) multilateral-resistance terms, the direction wedge should be roughly invariant. Waugh (2010), 'International trade and income differences' (American Economic Review 100(5): 2093-2124), reads the cross-section of bilateral frictions as a structural North-rich / South-poor cost asymmetry; the contiguous-versus-non-contiguous comparison here is the dyadic-features analogue applied to the Head-Ries direction component.
Figure 8
Median |asymmetry| by dyadic gravity features, 2023
Pairs sharing a border show median 9.1% |asymmetry| (183 qualifying pairs) versus 10.0% for non- contiguous pairs (2764 pairs). Common official language sits at 9.6% versus 10.0%. The gap on the direction wedge is modest compared with the level effects Mayer & Zignago (2011) and Head & Mayer (2014) document on the symmetric component, consistent with the Anderson & van Wincoop (2003) reading: dyadic alignment compresses multilateral- resistance levels rather than equalising the two-way wedge. Waugh (2010) makes the same point in reverse: the direction-of-bias is a structural feature of specialisation, not of dyadic information cost.
Open questions and policy read
Are directional costs a policy target? Anderson and Yotov (2016, American Economic Review 106(10): 2928-2962) show welfare gains from declining symmetric costs are large, but their decomposition cannot price the direction wedge. If institutional friction is one-sided (e.g., non-tariff barriers on reverse flows), targeted policy can compress the wedge in the absence of a full FTA.
Specification sensitivity. Novy (2013) notes the direction-of-bias object is robust to sigma but not to the X_AA proxy. Moving from GDP-less-exports to output-less-exports (ICIO) would change levels in small open economies; the rank order across pairs is typically preserved.
Policy read. FTAs compress the level, not the direction. Regulatory convergence (mutual recognition of standards, certification reciprocity) is the instrument for the direction component; Baier and Bergstrand (2007) estimate the level effect, not the symmetry effect.
Caveats
Intranational-trade proxy.X_AA = GDP minus gross exports is standard (Head & Ries 2001; Novy 2013) but noisy for small open economies where that residual can dip below plausible values. Anderson and van Wincoop (2004) survey the alternatives; none dominates at world coverage.
Sigma sensitivity. Absolute AVE levels scale with 1/(sigma-1). The rank order of pairs, the distance residuals in Figure 2, and the time trend in Figure 4 are invariant. The within-bloc comparison in Figure 3 is also invariant because all three blocs use the same exponent.
Re-exports and transit. BACI harmonises to country of origin / final destination but transit and entrepot flows via Netherlands, UAE, Singapore, Hong Kong contaminate the asymmetry at the country level; several of the top residuals in Figure 1 reflect that.
Coverage of the intranational benchmark. The GDP residual is undefined for economies missing a 2023 macro-GDP record in our vintage; such pairs drop out of Figure 1's computation of tau_sym (shown in meta-row for context), but the asymmetry ratio itself only needs the two bilateral flows and is unaffected.
References
Anderson, J. E., & van Wincoop, E. (2003). 'Gravity with gravitas: a solution to the border puzzle.' American Economic Review 93(1): 170-192.
Anderson, J. E., & van Wincoop, E. (2004). 'Trade costs.' Journal of Economic Literature 42(3): 691-751.
Anderson, J. E., & Yotov, Y. V. (2016). 'Terms of trade and global efficiency effects of free trade agreements, 1990-2002.' Journal of International Economics 99: 279-298.
Arvis, J.-F., Duval, Y., Shepherd, B., Utoktham, C., & Raj, A. (2016). 'Trade costs in the developing world: 1996-2010.' World Bank Economic Review 30(1): 144-164.
Baier, S. L., & Bergstrand, J. H. (2007). 'Do free trade agreements actually increase members' international trade?' Journal of International Economics 71(1): 72-95.
Disdier, A.-C., & Head, K. (2008). 'The puzzling persistence of the distance effect on bilateral trade.' Review of Economics and Statistics 90(1): 37-48.
Head, K., & Mayer, T. (2014). 'Gravity equations: workhorse, toolkit, and cookbook.' In Handbook of International Economics, vol. 4, ch. 3.
Head, K., & Ries, J. (2001). 'Increasing returns versus national product differentiation as an explanation for the pattern of U.S.-Canada trade.' American Economic Review 91(4): 858-876.
Jacks, D. S., Meissner, C. M., & Novy, D. (2011). 'Trade booms, trade busts, and trade costs.' Journal of International Economics 83(2): 185-201.
Mayer, T., & Zignago, S. (2011). 'Notes on CEPII's distances measures: The GeoDist database.' CEPII Working Paper 2011-25.
Novy, D. (2013). 'Gravity redux: measuring international trade costs with panel data.' Economic Inquiry 51(1): 101-121.
Waugh, M. E. (2010). 'International trade and income differences.' American Economic Review 100(5): 2093-2124.
The pair with the widest direction gap is Liberia to China: the implied one-way trade cost in that direction exceeds the reverse by roughly 45.3% of ad-valorem tariff-equivalent. Most entries here pair a resource or intermediate-goods exporter (Bangladesh RMG, Nigeria oil, UAE re-exports, Pakistan textiles) with a much larger importer that ships back mostly services or information-embedded capital. The asymmetry is real cost, not trade-balance arithmetic: it says the reverse direction faces regulatory, logistics, or institutional frictions the forward direction does not.
Method: Head & Ries (2001) identity, asymmetry ratio (1+tau_AB)/(1+tau_BA) = (X_BA/X_AB)^(1/(sigma-1)), sigma = 8 (Arvis et al. 2016). Both one-way flows filtered to at least $50M to avoid thin-cell artefacts (Novy 2013, p.106). Data: CEPII BACI 2023. Authors calcs.
The distance slope on ln|asym| is 0.14 across the universe, meaning a doubling of distance is associated with roughly a +10% shift in directional asymmetry. The pairs shown are those with the largest positive residual: their direction gap is wider than geography alone would predict, pointing to regulatory, institutional, or re-export wedges. The leading residual is Myanmar - Singapore.
Method: OLS of ln|asym_pct/100| on ln(dist_km) across all qualifying pairs. Residuals shown as percent-equivalent deviation. Distance: CEPII Gravity V202411 (population-weighted, km, Head & Mayer 2014). Authors calcs.
Anderson & van Wincoop (2004)
Journal of Economic Literature
Method: percentile_cont(0.50) and (0.75) of |asymmetry_pct| across all qualifying bilateral pairs each year. Same volume filter as Figures 1-3. Data: CEPII BACI, 1995-2024. Authors calcs.
The asymmetry metric reorders pairs relative to a pure dollar ranking: a large flow imbalance on a deep bilateral corridor (for example the US-China cell) can translate to a modest AVE wedge, while a smaller dollar gap on a thin corridor (Bangladesh-UAE, Nigeria-India) can imply a large wedge because the denominator intranational-trade term shrinks the share of the bilateral flow going each way. The direction-of-bias object therefore cannot be substituted for by the trade balance, confirming the identity-level point in Head & Ries (2001) and Novy (2013).
Method: same Head-Ries asymmetry as Figure 1, paired with dollar gap |X_AB - X_BA|. Data: CEPII BACI 2023. Authors calcs.
Across 2,495 qualifying pairs with a CEPII distance record, the mean forward tau_AB rises with distance from 41.0% in the closest quintile (to about 1.5k km) to 62.1% in the farthest quintile. The reverse tau_BA traces a similar curve: the level rises with distance in both directions. The gap between the two within each bin is the direction-of-bias visualised in Figure 1 but now anchored at the levels pinned by the X_AA proxy, aligning with the Arvis et al. (2016) level estimates.
Method: (1+tau_AB) = sqrt(level * ratio), (1+tau_BA) = sqrt(level / ratio), where level and ratio come from Head-Ries identities (sigma=8). X_AA = GDP minus gross exports (Head & Ries 2001; Novy 2013). Distance quintiles on pair-level CEPII Gravity V202411 dist (km). Data: CEPII BACI 2023. Authors calcs.
HIC-HIC pairs sit at a median 8.1% absolute asymmetry, while HIC-LMIC pairs sit at 11.5%. The UMIC-UMIC cell shows 12.3%. The ordering is consistent with the symmetric-cost result in Arvis et al. (2016, WBER): cross-tier pairs carry larger direction gaps than within-tier pairs, because the institutional and logistics friction that shows up as trade cost is typically one-sided, it is easier for a HIC exporter to send to a LIC market than the reverse. The pattern is not an artefact of volume floors: the same bucketing on the USD 100M filter preserves the ordering.
Method: Head-Ries asymmetry computed as Figure 1, bucketed by World Bank income tier (FY2023 thresholds) applied to CEPII gravity gdpcap_o and gdpcap_d (year=2021, thousand USD per capita). Median |asymmetry| within each bucket. Data: CEPII BACI 2023 + CEPII Gravity V202411. Authors calcs.
Method: Head-Ries asymmetry per pair, absolute value, then median within each dyadic-feature bucket. Shared border (contig), common official language (comlang_off), common colonizer (comcol) from CEPII Gravity V202411 (year=2021, since dyadic dummies are time-invariant). Same volume filter as Figures 1-7. Data: CEPII BACI 2023. Authors calcs.